X̄–R chart — synthetic shaft measurements
25 subgroups of five synthetic shaft diameter measurements. The last four subgroups contain a deliberate positive shift. Review both mean and range charts, selected signal rules, and the signal details. Control limits describe process behavior, not specification limits.
Guide · X̄–R chart · Run 1
X̄–R summary
| Statistic / setting | Value |
|---|---|
| Subgroups (k) | 25 |
| Subgroup size (n) | 5 |
| Grand mean (X̄̄) | 20 |
| Average R | 0.02586 |
| Within-subgroup σ | 0.01112 |
| Signals | 30 |
| Subgrouping | By subgroup label |
| 7-point trend | On |
| 6 on one side | On |
| 14 alternating | On |
| 2 of 3 beyond 2σ | On |
| 4 of 5 beyond 1σ | On |
Control limits and zones
| Statistic / setting | Value |
|---|---|
| X̄ CL | 20 |
| X̄ LCL | 19.99 |
| X̄ UCL | 20.02 |
| R CL | 0.02586 |
| R LCL | 0 |
| R UCL | 0.05466 |
| X̄ −1σ | 20 |
| X̄ +1σ | 20.01 |
| X̄ −2σ | 19.99 |
| X̄ +2σ | 20.01 |
Subgroup means and dispersion
| Subgroup index (as returned) | X̄ | R | X̄ signals | R signals |
|---|---|---|---|---|
| 1 | 20.01 | 0.0147 | None | None |
| 2 | 20.01 | 0.0294 | None | None |
| 3 | 20.01 | 0.0144 | None | None |
| 4 | 19.99 | 0.0363 | None | None |
| 5 | 20 | 0.0178 | None | None |
| 6 | 20 | 0.0191 | None | None |
| 7 | 20.01 | 0.0313 | None | None |
| 8 | 19.99 | 0.0283 | 6 on one side | None |
| 9 | 20 | 0.0348 | 6 on one side | None |
| 10 | 20 | 0.0321 | 6 on one side | None |
| 11 | 20 | 0.0351 | 4 of 5 beyond 1σ, 6 on one side | None |
| 12 | 19.99 | 0.0145 | 4 of 5 beyond 1σ, 6 on one side | None |
| 13 | 20 | 0.0371 | 6 on one side | None |
| 14 | 20 | 0.0291 | 4 of 5 beyond 1σ, 6 on one side | None |
| 15 | 20 | 0.0083 | 4 of 5 beyond 1σ, 6 on one side | None |
| 16 | 20 | 0.0271 | 6 on one side | None |
| 17 | 20 | 0.037 | 6 on one side | None |
| 18 | 20 | 0.033 | 6 on one side | None |
| 19 | 20 | 0.0342 | 6 on one side | None |
| 20 | 20 | 0.0164 | 6 on one side | None |
| 21 | 20 | 0.0148 | 6 on one side | None |
| 22 | 20.02 | 0.0186 | 2 of 3 beyond 2σ, 4 of 5 beyond 1σ, beyond limits | None |
| 23 | 20.03 | 0.0248 | 2 of 3 beyond 2σ, 4 of 5 beyond 1σ, beyond limits | None |
| 24 | 20.03 | 0.0382 | 2 of 3 beyond 2σ, 4 of 5 beyond 1σ, beyond limits | None |
| 25 | 20.03 | 0.02 | 2 of 3 beyond 2σ, 4 of 5 beyond 1σ, beyond limits | None |
Control chart signal details
| Index (as returned) | Chart | Rule |
|---|---|---|
| 8 | X̄ | 6 on one side |
| 9 | X̄ | 6 on one side |
| 10 | X̄ | 6 on one side |
| 11 | X̄ | 6 on one side |
| 11 | X̄ | 4 of 5 beyond 1σ |
| 12 | X̄ | 6 on one side |
| 12 | X̄ | 4 of 5 beyond 1σ |
| 13 | X̄ | 6 on one side |
| 14 | X̄ | 6 on one side |
| 14 | X̄ | 4 of 5 beyond 1σ |
| 15 | X̄ | 6 on one side |
| 15 | X̄ | 4 of 5 beyond 1σ |
| 16 | X̄ | 6 on one side |
| 17 | X̄ | 6 on one side |
| 18 | X̄ | 6 on one side |
| 19 | X̄ | 6 on one side |
| 20 | X̄ | 6 on one side |
| 21 | X̄ | 6 on one side |
| 22 | X̄ | beyond limits |
| 22 | X̄ | 2 of 3 beyond 2σ |
| 22 | X̄ | 4 of 5 beyond 1σ |
| 23 | X̄ | beyond limits |
| 23 | X̄ | 2 of 3 beyond 2σ |
| 23 | X̄ | 4 of 5 beyond 1σ |
| 24 | X̄ | beyond limits |
| 24 | X̄ | 2 of 3 beyond 2σ |
| 24 | X̄ | 4 of 5 beyond 1σ |
| 25 | X̄ | beyond limits |
| 25 | X̄ | 2 of 3 beyond 2σ |
| 25 | X̄ | 4 of 5 beyond 1σ |
X̄–R endpoint signal indices start at 1.
Mean chart (X̄)
Captured observations or subgroup means, control limits and signal markers in analysis order.
Range chart (R)
Captured within-subgroup variation or consecutive moving ranges with control limits and signal markers.